Invariant manifolds for impulsive equations and nonuniform polynomial dichotomies (Q609628)

For impulsive differential equations in Banach spaces, stable and unstable invariant manifolds are constructed by small perturbations of a polynomial dichotomy. The notions of polynomial Lyapunov exponent and regularity coefficient for a linear impulsive differential equation in a finite-dimensional space are introduced. It is proved that a linear impulsive differential equation admits a nonuniform polynomial dichotomy provided that its Lyapunov exponent does not vanish. Possible applications of the results to statistical physics and stochastic processes are briefly discussed.